Question

The value of ${\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)-{\sin }^{-1}\left(\frac{1}{2}\right)$ is

• A. $45°$
• B. $90°$
• C. $15°$
• D. $30°$

Answer 1

The correct option is D

$30°$

Explanation for the correct option

The given trigonometric expression: ${\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)-{\sin }^{-1}\left(\frac{1}{2}\right)$.

It is known that, $\sin \left(60°\right)=\frac{\sqrt{3}}{2}$.Thus, ${\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)=60°$.

It is also known that, $\sin \left(30°\right)=\frac{1}{2}$.Thus, ${\sin }^{-1}\left(\frac{1}{2}\right)=30°$.

Therefore, ${\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)-{\sin }^{-1}\left(\frac{1}{2}\right)=60°-30°$

$\Rightarrow {\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)-{\sin }^{-1}\left(\frac{1}{2}\right)=30°$.

Therefore, the value of ${\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)-{\sin }^{-1}\left(\frac{1}{2}\right)$ is $30°$.

Hence, the correct option is (D).